Finite Group Databasebeta

← C2×#13115068 #15863780

Subgroups — C2×#13115068 #15863780

Order 3328.

1478 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719209C211yesmaximal, characteristic
2C2×#11718625C211yesmaximal, characteristic, complemented
3C22×#88045C211yesmaximal, characteristic
4C2×#11718627C211yesmaximal, characteristic
5#13115068C218yesmaximal, direct product factor
6C2×#11718122C211yesmaximal, characteristic, complemented
7C2×#11718115C211yesmaximal, characteristic, complemented
8C2×C13×#382C211yesmaximal, characteristic, complemented
9C22×#6127C2211yescharacteristic
10C22×C13×C4⋊C4C2211yescharacteristic
11C22×C13×C4⋊C4C2211yescharacteristic
12C22×C42×C13C2211yescharacteristic
13C2×C4×C22⋊D13—22no—
14C2×#88180C2211yescharacteristic
15C22×#6099C2211yescharacteristic
16C22×#6099C2211yescharacteristic
17#11719209—22no—
18#11719209—22no—
19#11719209—22no—
20#11719209C2214yes—
21C2×#88147—21no—
22C2×#88146—21no—
23C2×C4⋊C4×D13—21no—
24C2×#88141—21no—
25C13×#382—22no—
26C13×#382C2214yescomplemented
27C2×C13×#95—22no—
28C2×#88050—21no—
29#11718627—22no—
30#11718627C2214yes—
31C2×#88049—21no—
32#11718625—22no—
33#11718625C2214yescomplemented
34C2×#88048—21no—
35C2×#88047—21no—
36C2×#88045C418yescomplemented
37C2×#88045C2214yes—
38#11718122C2214yescomplemented
39#11718115C2214yescomplemented
40C23×C4×C13—21no—
41C23×C4×C13—21no—
42C23×C4×C13D412yes—
43C23×C4×C13C2311yescharacteristic
44C22×C22⋊D13—21no—
45C2×#6127—21no—
46C2×#6127—21no—
47C2×#6127—22no—
48C2×#6127—22no—
49C2×#6127C2×C414yes—
50C2×#6127D412yes—
51C2×#6127Q814yes—
52C2×#6127C2312yes—
53C22×D52D411yescharacteristic
54C22×C4×D13—21no—
55C22×C4×D13—22no—
56C22×Dic26D411yescharacteristic
57C2×C13×C4⋊C4—21no—
58C2×C13×C4⋊C4—21no—
59C2×C13×C4⋊C4—21no—
60C2×C13×C4⋊C4—21no—
61C2×C13×C4⋊C4—21no—
62C2×C13×C4⋊C4—21no—
63C2×C13×C4⋊C4—21no—
64C2×C13×C4⋊C4—21no—
65C2×C13×C4⋊C4—21no—
66C2×C13×C4⋊C4D412yes—
67C2×C13×C4⋊C4C2312yes—
68C2×C13×C4⋊C4C2312yes—
69C2×C42×C13—21no—
70C2×C42×C13—22no—
71C2×C42×C13C2×C414yescomplemented
72C2×C42×C13C2312yes—
73C2×C22⋊Dic13—21no—
74C4×C22⋊D13—28no—
75C4×C22⋊D13—28no—
76C2×#6103—22no—
77#88180—21no—
78#88180—21no—
79#88180D412yes—
80#88180C2312yes—
81C2×C4⋊Dic13D411yescharacteristic
82C2×C4⋊Dic13D411yescharacteristic
83C2×#6101—22no—
84C2×C4×Dic13—22no—
85C2×C4×Dic13—21no—
86C2×#6099—21no—
87C2×#6099—22no—
88C2×#6099—21no—
89C2×#6099—22no—
90C2×#6099—22no—
91C2×#6099C2×C414yescomplemented
92C2×#6099C2312yes—
93C2×#6099C2312yes—
94C22×#1055—21no—
95C22×#1055—21no—
96#88147—24no—
97#88147—24no—
98#88146—24no—
99#88146—24no—
100C4⋊C4×D13—24no—
101C4⋊C4×D13—24no—
102#88141—24no—
103#88141—24no—
104C13×#95—28no—
105#88050—24no—
106#88049—24no—
107#88048—24no—
108#88047—24no—
109#88045C2×C4116yescomplemented
110C2×#1860—131nomaximal, Sylow
111C24×C13C2×D411yescharacteristic
112C23×D13—21no—
113C22×C4×C13—24no—
114C22×C4×C13—22no—
115C22×C4×C13—22no—
116C22×C4×C13—22no—
117C22×C4×C13—22no—
118C22×C4×C13—42no—
119C22×C4×C13—42no—
120C22×C4×C13—44no—
121C22×C4×C13—44no—
122C22×C4×C13—41no—
123C22×C4×C13—41no—
124C22×C4×C13C22×C412yes—
125C22×C4×C13C2×D411yescharacteristic
126C22×C4×C13C2×D411yescharacteristic
127C22×C4×C13C2×D411yescharacteristic
128C22×C4×C13C2×D411yescharacteristic
129C22×C4×C13C2×D414yes—
130C22×C4×C13C2×D411yescharacteristic
131C22×C4×C13C2×Q812yes—
132C22×C4×C13#4112yes—
133C22×C4×C13#4112yes—
134C22×C4×C13C2411yescharacteristic
135C2×C22⋊D13—24no—
136C2×C22⋊D13—22no—
137C2×C22⋊D13—24no—
138C2×C22⋊D13—22no—
139C22×Dic13—21no—
140C22×Dic13—21no—
141C22×Dic13—21no—
142#6127—24no—
143#6127—24no—
144#6127—24no—
145#6127—24no—
146#6127—24no—
147#6127—22no—
148#6127—22no—
149#6127C4⋊C418yes—
150#6127C22×C414yes—
151#6127C2×Q814yes—
152C2×D52—21no—
153C2×D52—22no—
154C2×D52C4⋊C414yes—
155C2×D52C2×D412yes—
156C2×C4×D13—24no—
157C2×C4×D13—22no—
158C2×C4×D13—24no—
159C2×C4×D13—22no—
160C2×C4×D13—28no—
161C2×C4×D13—84no—
162C2×Dic26—21no—
163C2×Dic26—22no—
164C2×Dic26C4⋊C414yes—
165C2×Dic26C2×D412yes—
166C13×C4⋊C4—22no—
167C13×C4⋊C4—22no—
168C13×C4⋊C4—22no—
169C13×C4⋊C4—22no—
170C13×C4⋊C4—22no—
171C13×C4⋊C4—22no—
172C13×C4⋊C4—41no—
173C13×C4⋊C4—41no—
174C42×C13—24no—
175C42×C13—22no—
176C42×C13C22×C414yescomplemented
177C22⋊Dic13—22no—
178C22⋊Dic13—22no—
179#6103—28no—
180C4⋊Dic13—21no—
181C4⋊Dic13—21no—
182C4⋊Dic13C2×D412yes—
183C4⋊Dic13C2×D412yes—
184#6101—28no—
185C4×Dic13—28no—
186C4×Dic13—22no—
187C4×Dic13—22no—
188#6099—24no—
189#6099—22no—
190#6099—22no—
191#6099—22no—
192#6099—42no—
193#6099C22×C414yescomplemented
194C2×#1055—24no—
195C2×#1055—22no—
196C2×#1055—22no—
197C2×#1055—42no—
198C2×#520—131no—
199C2×#428—131no—
200C22×#104—131no—
201C2×#417—131no—
202C2×#382D1311yescharacteristic, complemented
203#1860—138no—
204C2×#343—131no—
205C2×#339—131no—
206C23×C13—22no—
207C23×C13—22no—
208C23×C13C4×D412yes—
209C23×C13#12011yescharacteristic
210C23×C13#12011yescharacteristic
211C23×C13C22⋊Q812yes—
212C23×C13C22×D411yescharacteristic
213C22×D13—22no—
214C22×D13—24no—
215C22×D13—42no—
216C22×D13—42no—
217C2×C4×C13—24no—
218C2×C4×C13—24no—
219C2×C4×C13—48no—
220C2×C4×C13—42no—
221C2×C4×C13—42no—
222C2×C4×C13—44no—
223C2×C4×C13—44no—
224C2×C4×C13—44no—
225C2×C4×C13—42no—
226C2×C4×C13—82no—
227C2×C4×C13—82no—
228C2×C4×C13—82no—
229C2×C4×C13C2×C4⋊C412yes—
230C2×C4×C13C2×C4⋊C412yes—
231C2×C4×C13C4×D412yes—
232C2×C4×C13C4×D412yes—
233C2×C4×C13C4×D412yes—
234C2×C4×C13#12011yescharacteristic
235C2×C4×C13#12011yescharacteristic
236C2×C4×C13C22⋊Q812yes—
237C2×C4×C13C22⋊Q812yes—
238C2×C4×C13C22⋊Q812yes—
239C2×C4×C13#12312yes—
240C2×C4×C13#12312yes—
241C2×C4×C13C23×C411yescharacteristic
242C2×C4×C13C22×D411yescharacteristic
243C2×C4×C13C22×D411yescharacteristic
244C2×C4×C13C22×Q811yescharacteristic
245C2×C4×C13C2×#4111yescharacteristic
246C2×C4×C13C2×#4111yescharacteristic
247C22⋊D13—24no—
248C22⋊D13—24no—
249C22⋊D13—28no—
250C2×Dic13—22no—
251C2×Dic13—24no—
252C2×Dic13—22no—
253C2×Dic13—22no—
254C2×Dic13—42no—
255C2×Dic13—42no—
256D52—22no—
257D52—24no—
258D52C2×C4⋊C414yes—
259C4×D13—24no—
260C4×D13—24no—
261C4×D13—28no—
262C4×D13—88no—
263Dic26—22no—
264Dic26—24no—
265Dic26C2×C4⋊C414yes—
266#1055—24no—
267#1055—42no—
268C22×#41—131no—
269C22×M16—131no—
270C22×M16—131no—
271#520—134no—
272#520—262no—
273#520—262no—
274#520—262no—
275C2×C4×Q8—261no—
276C2×C4×D4—261no—
277C2×C4×D4—262no—
278C2×#117—131no—
279C2×#117—261no—
280C22×C4⋊C4—261no—
281C22×C4⋊C4C2×D1311yescharacteristic
282C22×C4⋊C4C2×D1311yescharacteristic
283C22×C42C2×D1311yescharacteristic
284#428—134no—
285#428—262no—
286C2×#107—261no—
287C2×#106—261no—
288C2×#104—138no—
289C2×#104—134no—
290#417—134no—
291#417—262no—
292C2×#103—261no—
293C2×#102—261no—
294#382—22no—
295#382C2×D1314yescomplemented
296C2×#95—22no—
297#343—134no—
298#339—134no—
299C22×C13—24no—
300C22×C13—24no—
301C22×C13—21no—
302C22×C13—21no—
303C22×C13—21no—
304C22×C13—21no—
305C22×C13#38512yes—
306C22×C13#38512yes—
307C22×C13#45412yes—
308C22×C13#45512yes—
309C22×C13C2×C4×D411yescharacteristic
310C22×C13C2×#12011yescharacteristic
311C22×C13C2×C22⋊Q811yescharacteristic
312C2×D13—24no—
313C2×D13—48no—
314C2×D13—42no—
315C2×D13—42no—
316C4×C13—44no—
317C4×C13—44no—
318C4×C13—82no—
319C4×C13#38512yes—
320C4×C13#38512yes—
321C4×C13C22×C4⋊C411yescharacteristic
322C4×C13C2×C4×D411yescharacteristic
323C4×C13C2×C22⋊Q811yescharacteristic
324C4×C13C2×#12311yescharacteristic
325Dic13—24no—
326Dic13—42no—
327Dic13—42no—
328C2×#41—134no—
329C2×#41—132no—
330C2×#41—134no—
331C2×#41—132no—
332C2×#41—262no—
333C2×#41—261no—
334C2×#41—262no—
335C2×#41—261no—
336C22×Q8—131no—
337C22×D4—131no—
338C22×D4—261no—
339C23×C4—21no—
340C23×C4—21no—
341C23×C4—262no—
342C23×C4—261no—
343C23×C4C22⋊D1312yes—
344C23×C4C22×D1311yescharacteristic
345C2×M16—134no—
346C2×M16—132no—
347C2×M16—132no—
348C2×M16—261no—
349C2×M16—262no—
350C2×M16—261no—
351C2×M16—262no—
352C2×M16—262no—
353C22×C8—261no—
354C22×C8—261no—
355C4×Q8—264no—
356C4×Q8—264no—
357C4×D4—264no—
358C4×D4—264no—
359C4×D4—268no—
360C4×D4—268no—
361#117—132no—
362#117—132no—
363#117—264no—
364#117—264no—
365#117—261no—
366#117—261no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—131no—
377C2×C4⋊C4—131no—
378C2×C4⋊C4—264no—
379C2×C4⋊C4—264no—
380C2×C4⋊C4—262no—
381C2×C4⋊C4C22⋊D1312yes—
382C2×C4⋊C4C22×D1312yes—
383C2×C4⋊C4C22×D1312yes—
384C2×C22⋊C4—262no—
385C2×C22⋊C4—261no—
386C2×C42—22no—
387C2×C42—21no—
388C2×C42—262no—
389C2×C42—261no—
390C2×C42C4×D1314yescomplemented
391C2×C42C22×D1312yes—
392#107—264no—
393#106—264no—
394#104—1316no—
395#103—264no—
396#102—264no—
397#95—28no—
398C2×C13—21no—
399C2×C13—21no—
400C2×C13—22no—
401C2×C13#186014yescomplemented
402C2×C13C2×#38511yescharacteristic
403C2×C13C2×#45511yescharacteristic
404C2×C13C2×#45411yescharacteristic
405D13—44no—
406C24—261no—
407C24C2×C22⋊D1311yescharacteristic
408#41—138no—
409#41—134no—
410#41—134no—
411#41—264no—
412#41—264no—
413#41—264no—
414#41—264no—
415#41—264no—
416#41—262no—
417#41—262no—
418C2×Q8—134no—
419C2×Q8—132no—
420C2×Q8—262no—
421C2×Q8—261no—
422C2×D4—134no—
423C2×D4—132no—
424C2×D4—264no—
425C2×D4—262no—
426C2×D4—264no—
427C2×D4—262no—
428C2×D4—262no—
429C2×D4—261no—
430C22×C4—24no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—42no—
436C22×C4—42no—
437C22×C4—44no—
438C22×C4—44no—
439C22×C4—41no—
440C22×C4—41no—
441C22×C4—268no—
442C22×C4—261no—
443C22×C4—264no—
444C22×C4—264no—
445C22×C4—262no—
446C22×C4—262no—
447C22×C4—261no—
448C22×C4—261no—
449C22×C4—1044no—
450C22×C4C2×C4×D1312yes—
451C22×C4#612712yes—
452C22×C4D4×D1311yescharacteristic
453C22×C4D4×D1311yescharacteristic
454C22×C4D4×D1311yescharacteristic
455C22×C4D4×D1311yescharacteristic
456C22×C4Q8×D1312yes—
457C22×C4#613112yes—
458C22×C4C2×C22⋊D1314yes—
459C22×C4C2×C22⋊D1311yescharacteristic
460C22×C4C23×D1311yescharacteristic
461M16—134no—
462M16—264no—
463M16—262no—
464M16—262no—
465M16—262no—
466M16—522no—
467C2×C8—264no—
468C2×C8—262no—
469C2×C8—262no—
470C2×C8—522no—
471C4⋊C4—22no—
472C4⋊C4—22no—
473C4⋊C4—22no—
474C4⋊C4—22no—
475C4⋊C4—22no—
476C4⋊C4—22no—
477C4⋊C4—41no—
478C4⋊C4—41no—
479C4⋊C4—132no—
480C4⋊C4—132no—
481C4⋊C4—268no—
482C4⋊C4—261no—
483C4⋊C4—261no—
484C22⋊C4—268no—
485C22⋊C4—262no—
486C22⋊C4—262no—
487C42—24no—
488C42—22no—
489C42—268no—
490C42—262no—
491C42—262no—
492C42C2×C4×D1314yescomplemented
493C13C2×#186011yescharacteristic, complemented, Sylow
494C23—22no—
495C23—22no—
496C23—262no—
497C23—264no—
498C23—522no—
499C23—522no—
500C23C4×C22⋊D1312yes—
501C23#8819111yescharacteristic
502C23#8819111yescharacteristic
503C23#8820012yes—
504C23C22×C22⋊D1311yescharacteristic
505Q8—134no—
506Q8—262no—
507Q8—264no—
508D4—134no—
509D4—264no—
510D4—264no—
511D4—268no—
512D4—262no—
513D4—264no—
514C2×C4—24no—
515C2×C4—24no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—48no—
519C2×C4—44no—
520C2×C4—44no—
521C2×C4—44no—
522C2×C4—42no—
523C2×C4—82no—
524C2×C4—82no—
525C2×C4—82no—
526C2×C4—262no—
527C2×C4—264no—
528C2×C4—264no—
529C2×C4—264no—
530C2×C4—268no—
531C2×C4—262no—
532C2×C4—262no—
533C2×C4—522no—
534C2×C4—522no—
535C2×C4—1048no—
536C2×C4C4⋊C4×D1312yes—
537C2×C4C4⋊C4×D1312yes—
538C2×C4#8814712yes—
539C2×C4#8814712yes—
540C2×C4#8814812yes—
541C2×C4#8814812yes—
542C2×C4#8815012yes—
543C2×C4#8815012yes—
544C2×C4C4×C22⋊D1312yes—
545C2×C4#8819111yescharacteristic
546C2×C4#8819111yescharacteristic
547C2×C4#8820012yes—
548C2×C4C22×C4×D1311yescharacteristic
549C2×C4C2×#612711yescharacteristic
550C2×C4C2×D4×D1311yescharacteristic
551C2×C4C2×D4×D1311yescharacteristic
552C2×C4C2×Q8×D1311yescharacteristic
553C2×C4C2×#613111yescharacteristic
554C8—264no—
555C8—522no—
556C22—21no—
557C22—21no—
558C22—21no—
559C22—21no—
560C22—24no—
561C22—24no—
562C22—264no—
563C22—522no—
564C22—522no—
565C22—528no—
566C22#1171865012yes—
567C22#1171865012yes—
568C22#1171872212yes—
569C22#1171872312yes—
570C22C2×C4×C22⋊D1311yescharacteristic
571C22C2×#8819111yescharacteristic
572C22C2×#8820011yescharacteristic
573C4—44no—
574C4—44no—
575C4—82no—
576C4—264no—
577C4—522no—
578C4—522no—
579C4#1171865012yes—
580C4#1171865012yes—
581C4C2×C4⋊C4×D1311yescharacteristic
582C4C2×#8814711yescharacteristic
583C4C2×#8814811yescharacteristic
584C4C2×#8815011yescharacteristic
585C2—21no—
586C2—21no—
587C2—22no—
588C2—524no—
589C2#1311506814yesdirect product factor
590C2C2×#1171865011yescharacteristic
591C2C2×#1171872211yescharacteristic
592C2C2×#1171872311yescharacteristic
subgroupG/H
centerC23#88191
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC2×C13×#382C2
socleC23×C13#120
prime radicalC22×#6127C22
cosocleC22×C4×C13C24
hypercenterC2×#382D13
hypocenterC13C2×#1860
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#382

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#11718625C2semidirect
5. #13115068C2direct (N × H)
6. C2×#11718122C2semidirect
7. C2×#11718115C2semidirect
8. C2×C13×#382C2semidirect
26. C13×#382C22semidirect
33. #11718625C22semidirect
36. C2×#88045C4semidirect
38. #11718122C22semidirect
39. #11718115C22semidirect
71. C2×C42×C13C2×C4semidirect
91. C2×#6099C2×C4semidirect
109. #88045C2×C4semidirect
176. C42×C13C22×C4semidirect
193. #6099C22×C4semidirect
202. C2×#382D13semidirect
295. #382C2×D13semidirect
390. C2×C42C4×D13semidirect
401. C2×C13#1860semidirect
492. C42C2×C4×D13semidirect
493. C13C2×#1860semidirect
589. C2#13115068direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#117192092
C2×#117186252
C22×#880452
C2×#117186272
#131150682
C2×#117181222
C2×#117181152
C2×C13×#3822
C2×#186013